what is the equation of the graph below?

Explanation:

Step1: Identify the general form of a cosine - type function

The general form of a cosine function is $y = A\cos(Bx - C)+D$.

Step2: Determine the amplitude $A$

The amplitude is half of the vertical distance between the maximum and minimum values. The maximum value is $y = 1$ and the minimum value is $y=-1$. So, $A=\frac{1 - (- 1)}{2}=1$.

Step3: Determine the period $T$ and find $B$

The period $T$ is the horizontal distance between two consecutive maxima or minima. Here, $T = 2\pi$. Since the formula for the period of $y = A\cos(Bx - C)+D$ is $T=\frac{2\pi}{|B|}$, and $T = 2\pi$, then $|B| = 1$. Since there is no horizontal compression or stretch, $B = 1$.

Step4: Determine the phase - shift $C$

The graph is not shifted horizontally. So, $C = 0$.

Step5: Determine the vertical - shift $D$

The mid - line of the graph is $y = 0$. So, $D = 0$.

Answer:

$y=\cos(x)$